FIG. 8 is a block diagram showing an example of a conventional target tracking device. This target tracking device comprises a passive sensor 1, a tracking processor 2, and a control unit 3. The passive sensor 1 measures the angle of a radio wave, infrared rays, a sound wave, or the like radiated (and reradiated) from a target. That is, the passive sensor 1 measures the angle of the target, thereby obtaining angular measurement. The passive sensor 1 sends the angular measurement to the tracking processor 2.
The tracking processor 2 calculates a predicted state and an updated state based on the angular measurement from the passive sensor 1. The tracking processor 2 sends the predicted state and the updated state to the control unit 3 as the target track. Based on the target track from the tracking processor 2, the control unit 3 generates a control signal to control the posture and the like of the passive sensor 1, and sends the signal to the passive sensor 1.
FIG. 9 is a flowchart illustrating the procedure executed by the conventional target tracking device.
When target tracking processing starts, angular measurement is input to the tracking processor 2 (ST101). That is, the passive sensor 1 measures the target based on the control signal from the control unit 3, and sends the angular measurement of the target obtained by the measurement to the tracking processor 2. The tracking processor 2 acquires the angular measurement sent from the passive sensor 1.
Prediction processing is executed (ST102). That is, the tracking processor 2 calculates the predicted state of the target and its covariance matrix based on the updated state of the target and its covariance matrix calculated in step ST103 of the preceding measurement.
Update processing is then executed (ST103). That is, based on the angular measurement of the target from the passive sensor 1 and the predicted state of the target and its covariance matrix calculated in step ST102, the tracking processor 2 calculates the updated state of the target and its covariance matrix and sends them to the control unit 3 as the target track.
Control processing is executed (ST104). That is, based on the target track from the tracking processor 2, the control unit 3 generates a control signal to control the posture and the like of the passive sensor 1, and sends the signal to the passive sensor 1. The processing of steps ST101 to ST105 is continued until the end.
The processing contents of the tracking processor 2 will be described in detail. The motion model of the target is defined in the following way. Note that “bar x” will be expressed as “x(-)” hereinafter.
                                          x            _                                k            +            1                          =                                            F                              k                +                1                                      ⁢                                          x                _                            k                                +                                    G                              k                +                1                                      ⁢                          W              k                                                          (        1        )                                                      x            _                    k                =                  [                                                                      a                  k                                                                              e                  k                                                                                                  a                    .                                    k                                                                                                                                                e                        .                                            k                                        ]                                    T                                                                                        (        2        )                                          F                      k            +            1                          =                  [                                                                      I                  2                                                                                                  (                                                                  t                                                  k                          +                          1                                                                    -                                              t                        k                                                              )                                    ·                                      I                    2                                                                                                                        O                  2                                                                              I                  2                                                              ]                                    (        3        )                                          G                      k            +            1                          =                  [                                                                                                                                        (                                                                              t                                                          k                              +                              1                                                                                -                                                      t                            k                                                                          )                                            2                                        2                                    ·                                      I                    2                                                                                                                                            (                                                                  t                                                  k                          +                          1                                                                    -                                              t                        k                                                              )                                    ·                                      I                    2                                                                                ]                                    (        4        )                                          Q          k                =                              1                          r              k                                ⁡                      [                                                                                                      (                                              σ                        k                        h                                            )                                        2                                                                    0                                                                              0                                                                                            (                                              σ                        k                        v                                            )                                        2                                                                        ]                                              (        5        )            where x(-)k is a state vector including an azimuth ak, an elevation ek, and their velocity components at an measurement time tk, Fk+1 and Gk+1 are the transition matrix and the driving matrix from the measurement time tk to an measurement time tk+1, respectively, wk is the process noise vector at the measurement time tk for an average 0 and a covariance matrix Qk, σhk and σvk are the standard deviations of the horizontal and vertical planes of process noise at the measurement time tk, respectively, rk is the distance from the passive sensor 1 to the target at the measurement time tk, AT is the transposition of a vector or matrix A, In is an n×n identity matrix, and On is an n×n zero matrix.
The measurement model of the passive sensor 1 is defined by
                              y          k                =                                            H              k                        ⁢                                          x                _                            k                                +                      v            k                                              (        6        )                                          H          k                =                  [                                                    1                                            0                                            0                                            0                                                                    0                                            1                                            0                                            0                                              ]                                    (        7        )                                          R          k                =                  [                                                                                          (                                          σ                      k                      a                                        )                                    2                                                            0                                                                    0                                                                                  (                                          σ                      k                      e                                        )                                    2                                                              ]                                    (        8        )            where yk is the measurement vector of the passive sensor 1 at the measurement time tk, Hk is the measurement matrix of the passive sensor 1 at the measurement time tk, vk is the measurement noise vector of the passive sensor 1 at the measurement time tk for an average 0 and a covariance matrix Rk, and σak and σek are the standard deviations of the azimuth and elevation of measurement noise at the measurement time tk, respectively.
In step ST101, the angular measurement from the passive sensor 1 is input as the measurement vector yk.
In step ST102, prediction processing represented by the following equations is executed using the result of update processing of the preceding measurement. Note that “hat x” will be expressed as “x(^)” hereinafter.
                                          x            ^                                k            |                          k              -              1                                      =                              F            k                    ⁢                                    x              ^                                                      k                -                1                            |                              k                -                1                                                                        (        9        )                                          P                      k            |                          k              -              1                                      =                                            F              k                        ⁢                                                            P                                                            k                      -                      1                                        |                                          k                      -                      1                                                                      ⁡                                  (                                      F                    k                                    )                                            T                                +                                    G              k                        ⁢                                                            Q                                      k                    -                    1                                                  ⁡                                  (                                      G                    k                                    )                                            T                                                          (        10        )                                          Q                      k            -            1                          =                              1                          r              preset                                ⁡                      [                                                                                                      (                                              σ                                                  k                          -                          1                                                h                                            )                                        2                                                                    0                                                                              0                                                                                            (                                              σ                                                  k                          -                          1                                                v                                            )                                        2                                                                        ]                                              (        11        )            where x(^)k|k−1 and Pk|k−1 are the predicted state vector and the predicted error covariance matrix at the measurement time tk, respectively, and x(^)k−1|k−1 and Pk−1|k−1 are the updated state vector and the updated error covariance matrix at an measurement time tk−1, respectively. Since a true value rk−1 of the target distance cannot be known, a preset target distance rpreset is used when calculating a process noise covariance matrix Qk−1.
In step ST103, update processing represented by the following equations is executed using the measurement vector from the passive sensor 1 and the result of prediction processing. Note that “tilde y” will be expressed as “y(˜)” hereinafter.{tilde over (y)}k=yk−Hk{circumflex over (x)}k|k−1  (12)Sk=HkPk|k−1(Hk)T+Rk  (13)Kk=Pk|k−1(Hk)T(Sk)−1  (14){circumflex over (x)}k|k={circumflex over (x)}k|k−1+Kk{tilde over (y)}k  (15)Pk|k=(I4−KkHk)Pk|k−1  (16)where y(˜)k is the residual vector of the passive sensor 1 at the measurement time tk, Sk is the residual covariance matrix of the passive sensor 1 at the measurement time tk, Kk is the Kalman gain matrix of the passive sensor 1 at the measurement time tk, x(^)k|k and Pk|k are the updated state vector and the updated error covariance matrix at the measurement time tk, respectively, and A−1 is the inverse matrix of the matrix A.
As described above, in the tracking processing of the passive sensor 1, the process noise covariance matrix Qk−1 includes an error because the distance data from the passive sensor 1 to the target is not available. It is consequently difficult to calculate the optimum value of the filter gain (Kalman gain matrix) that is indirectly calculated from the process noise covariance matrix and used to calculate the track. Hence, the track error of the target becomes large.
Even for a target that performs constant velocity (non-maneuver) on the orthogonal coordinate system, an angular acceleration and the differential component of the angular acceleration are generated on the polar coordinate system. Since it is difficult to estimate the component from angular measurement and reflect it on the process noise covariance matrix Qk−1, the track error becomes large.
As a technique of improving the tracking performance for both a target that performs non-maneuver and a target that performs maneuver, an Interacting Multiple Model (IMM) filter is known, which operates a plurality of motion models in parallel. However, since many motion models are generally defined as a motion on a three-dimensional orthogonal coordinate system, it is difficult to apply the technique to the tracking processor 2 that estimates the target track on a two-dimensional polar coordinate system or the like.
As described above, in the target tracking device using a passive sensor, the distance data from the passive sensor 1 to the target is not obtained in general. It is therefore difficult to calculate the optimum value of the filter gain to be used to calculate the track, and the track error becomes large.
Since the distance data to the target cannot be obtained, the target is tracked on a local coordinate system about the passive sensor. However, when, for example, a polar coordinate system is used as the local coordinate system, an angular acceleration and the differential component of the angular acceleration are generated on the polar coordinate system even if the target performs constant velocity (non-maneuver) on the orthogonal coordinate system.
When the filter gain is increased to cope with the above-described problem, the random component of the track error becomes large. When the filter gain is decreased to make the random component of the track error smaller, the bias component of the track error becomes large. At any rate, it is difficult to improve the tracking performance.
When a technique assuming a single motion model is optimized for a target that performs non-maneuver, tracking performance for a target that performs maneuver degrades. Similarly, when the technique is optimized for a target that performs maneuver, tracking performance for a target that performs non-maneuver degrades. That is, it is difficult for the existing technique to improve the tracking performance for both a target that performs non-maneuver and a target that performs maneuver.